Faddeev Formalism Research Articles

Spurious states in the Faddeev formalism for few-body systems

We discuss the appearance of spurious solutions of few-body equations for Faddeev amplitudes. The identification of spurious states, i.e., states that lack the symmetry required for solutions of the Schroedinger equation, as well as the symmetrization of the Faddeev equations is investigated. As an example, systems of three and four electrons, bound in a harmonic-oscillator potential and interacting by the Coulomb potential, are presented.

Spectrum and Static Properties of Heavy Baryons

Using several realistic interquark potentials, the ground-state energies of all the baryons containing one, two or three heavy quarks of type c or b are studied within a non-relativistic quark model. The three-body problem is rigorously solved using the Faddeev formalism. Various static properties, such as mass radii, charge radii, magnetic moments, and wave functions at the origin are calculated as well. The complete spectrum for all these baryons is computed using a harmonic-oscillator basis with states up to 8 quanta. Emphasis is put on the levels lying below the thresholds corresponding to quark-pair creation.

Spectroscopy of baryons containing heavy quarks

The ground state properties of heavy baryons (containing at least one quark of type c or b) are studied in a non-relativistic frame using a realistic interquark potential and the Faddeev formalism to solve the three-body problem. The complete spectra are computed by diagonalisation in a harmonic oscillator basis up to 8 quanta. Emphasis is put on the resonances lying below the thresholds corresponding to a quark pair creation.

Nucleon-Trinucleon Scattering in Terms of the Schmidt Expansion. I

In order to define the elastic/rearrangement and the breakup amplitudes for nucleon-trinucleon (NT) scattering in conformity with Faddeev's residue prescription, a pole term decomposition of the amplitudes for 3 + 1 and 2 + 2 subsystems is introduced. New Osborn-type equations for these four-nucleon amplitudes are derived. The obtained Osborn equations are expressed in practical form using the Schmidt expansion for each subamplitude. In order to clarify the difference between Faddeev's formalism and the previously proposed one based on the various pole expansions, a detailed comparison of them is made.

α-α-Λ Model Calculation of ^9_ΛBe Hypernucleus by the Three-Body Faddeev Formalism

α-α-Λ Model Calculation of ^9_ΛBe Hypernucleus by the Three-Body Faddeev Formalism

Shell model states in the 18O three-body wave function.

A study is made of shell model state structures present in the three-body wave functions of low-lying positive parity levels of {sup 18}O calculated with the Faddeev formalism.

The K−-deuteron interaction below 1 GeV/c

We have analysed the K− d-induced reactions both in flight and for K− capture from rest. The two-body hadronic interactions have been adopted in the form of a rank-one separable potential whose parameters have been adjusted to fit two-body scattering data. The in-flight reaction cross-sections are obtained from the distorted-wave impulse approximation whereas the at-rest capture rates are calculated from the appropriate multichannel Faddeev formalism. The calculated spectra are in good quantitative agreement with the data. The prominent peak at 2130 MeV in the lambdaproton effective mass distribution is interpreted as a strong cusp effect which requires the existence of a pole in the hyperon-nucleon scattering amplitude close to sigma-nucleon threshold. The excitation at 2140 MeV can be reproduced by assuming a narrowp-wave hyperon-nucleon resonance similar to that predicted by quark model asq2-q4,L=1 orbital excitation.

Structure of 9Be Nucleus Using the Generator Coordinate Method and the Three-Body Model

The structure of the 9Be nucleus is considered as being composed of three clusters (two alpha particles and a neutron). The bound state of the 9Be nucleus is studied using the approaches of the generator coordinate method as well the three-body model formalism. The numerical calculations are carried out using different types of two-body interactions. Yamaguchi, Gaussian, Tabakin and Volkov type potentials are used. The three-body model is also used in treating the three clusters forming the 9Be nucleus by following the Faddeev formalism. In both approaches, the low-lying energy levels of the 9Be nucleus as well as its binding energy are numerically calculated. Good agreements are obtained between the present theoretically calculated values and the experimental data.

Total disintegration of three-nucleon systems from charged π-mesons reactions

The nuclear reactions of incident charged π-mesons on three-nucleon system targets are considered. The double charge exchange process is considered for these reactions. The double charge exchange reactions of charged π+ and π- mesons on the3H and3He nuclei proceed through the only channel of total disintegration of these nuclei, leading to the final states of free three protons or three neutrons, respectively. The same Hamiltonian and the same nucleon-nucleon interaction are used in representing the initial and final nuclear states. The Faddeev formalism is used in describing the three nucleons. Numerical calculations are carried out for the differential and total cross-sections using different nucleon-nucleon potentials. The present theoretical calculations are in good agreement with the experimental data.

Role of three-body correlations in recombination of spin-polarized atomic hydrogen.

We present results of a calculation of the volume rate constant Lgeff of dipole recombination in H↓↓, in which the bbb incoming state is determined exactly by means of the Faddeev formalism. Inclusion of all three-particle correlations in the initial state does not resolve the discrepancies between Kagan’s approach and experiment. As a first step towards an exact determination of the outgoing atom-molecule state, we present a calculation in which all three-particle collision aspects are taken into account, except for rearrangement. This leads to values for Lgeff, which are a factor of 5 smaller than experiment, while the B dependence of the rate constant still shows a slowly increasing behavior. On the basis of this state-of-the-art calculation, we thus localize the cause for the existing discrepancies in rearrangement processes.

Coulomb Forces in Three Charged Particles Interacting via Stripping Nuclear Reactions

AbstractCoulomb forces are examined for three charged interacting particles following the Faddeev formalism. Application of stripping nuclear reactions is studied for 6Li projectile incident on 12C target with alpha particle transfer. Differential corss‐sections are calculated. The results are found to be improved by about 12.41% due to the inclusion of the Coulomb forces.

3-Alpha cluster Faddeev calculation and effects of three-body force

The three-alpha model of 12C nucleus is investigated by using the Faddeev formalism with the Pauli correct alpha-alpha potential. Almost all of the important low-lying levels are obtained successfully, in which any spurious states do not appear in our calculation. Furthermore, effects of three-body force are investigated with a simple Gaussian type three-cluster potential. It is found that the three-cluster force is very important, as well as the Coulomb force, to obtain the right order of energy spectra of 12C nucleus. Our final results with those full potentials show good agreement with experimental spectra.

Dependence of the Three‐Nucleon Binding Energy on Some Different Effects

AbstractThe bound state of three‐nucleon system is studied as a three‐body problem which is solved following the different approaches of the Faddeev formalism as well as the unitary pole approximation. The three‐body problem is reduced to a set of coupled integral equations by using separable approximations. Numerical calculations are carried out for the resulting integral equations and the separable expansion. In the present work, we calculate the ground‐state binding energy of the bound three‐nucleon system 3H. The main interest of the present work is to investigate the sensitivity of the three‐nucleon binding energy to different effects. For this reason, we study the dependence of this energy on different forms of local and separable nucleon‐nucleon potentials, the effective range of the nucleon‐nucleon interaction, and on the percent of the D state in the deuteron wave function. Also we test the sensitivity of the three‐nucleon binding energy to the considered number of terms from the separable expansion.

Quantum mechanical reactive scattering theory

AbstractIn this article we briefly discuss a number of promising approaches to the formulation of a general, numerically exact, quantum mechanical theory of fully three‐dimensional reactive atom‐diatom collisions. It is noted that the ability to treat the three‐dimensional H + H2 exchange reactions is pre‐requisite to any demonstration of the success of a general quantum mechanical formalism for reactivescattering. However, it is also noted that the time has come for any such theory to further demonstrate the ability to go beyond this basic, elementary atom‐diatom exchange reaction. It is speculated that there now exist a number of approaches which can potentially provide such a general framework for quantum reactive scattering theory. Finally, a new generalizationof the Faddeev formalism for such systems, which is capable of inclusion ofthree body forces with a completely general form for the potential surface, is presented.

Faddeev calculations in the three-particle model for theA=18 system: Energy levels of18F

The nucleus18F is treated as an inert core of16O plus two valence nucleons. TheT=0 andT=1 states are investigated using the Faddeev formalism. The calculated energy spectrum is similar to that obtained with shell model calculations.

Special Features of the Alpha Induced Deuteron Breakup

The alpha induced deuteron breakup reactions have been of interest since the nucleon induced deuteron breakup problem was addressed with tractable and predictive models based on the Faddeev formalism and with appropriate nucleon-nucleon forces. In this paper we discuss a few special features of the alpha induced deuteron breakup reactions. Specifically, we point out the importance of the n-p tensor force in the predictions of the three-body model that fit the tensor analyzing powers better and the concomitant deterioration of the fit to the vector analyzing power caused by the inclusion of the tensor force. We suggest that there exists evidence for the 1S0 n-p interaction, which is isospin forbidden, in both the cross section and spin observables data. Finally, we discuss certain characteristics of the p-α quasi-free-scattering and n-p final-state-interaction processes.

Possible existence of aπ−nnbound state

We have applied the relativistic Faddeev formalism to look for a bound state of a negative pion and two neutrons, using as input the pion-nucleon ${P}_{33}$ channel and the nucleon-nucleon $^{1}S_{0}$ channel. We found that if the pion-nucleon interaction is sufficiently short ranged, the system can be bound. We represented the pion-nucleon interaction with two different models of rank-one separable potentials, while for the nucleon-nucleon interaction we used the Yamaguchi potential and three different models of rank-two separable potentials.NUCLEAR REACTIONS ${\ensuremath{\pi}}^{\ensuremath{-}}\mathrm{nn}$ bound state; calculated, Fredholm determinant at $\sqrt{S}=2018$ MeV.

Properties of solutions for N-body Yakubovskii–Faddeev equations

We give a revised presentation of the Yakubovskii–Faddeev formalism based on a systematic study of the N-body system chain structure. Completeness properties of the corresponding equations in differential form are considered. The expressions of physical and spurious solutions are given in terms of the N-body asymptotic partition Hamiltonians eigenvectors.

On light supernuclei

The possible existence of charmed analogues of the YN and light hypernuclear systems are investigated using phenomenological one-boson-exchange potential and the SU(4) symmetry. Bound light supernuclei such as C1N (I=3/2, J=0) and C1NN(I=2, J=1/2) C0NN (I=1, J=1/2, and I=0, J=1/2 or 3/2) are predicted with reasonable binding energies using Faddeev formalism for the three body systems.

Test of Hadronic Charge Symmetry by Pion Scattering on Deuterium

A sensitive test of hadronic charge symmetry has been made by comparing differential cross sections for ${\ensuremath{\pi}}^{+}$ and ${\ensuremath{\pi}}^{\ensuremath{-}}$ elastic scattering from deuterium at 143 MeV. Coulomb effects were calculated with the three-body Faddeev formalism. After corrections for Coulomb effects the cross-section ratio indicates that charge symmetry is valid to within (0.4\ifmmode\pm\else\textpm\fi{}0.5)%.